Answer:
(x - 1)² + (y + 1/2)² = 65/4
Step-by-step explanation:
Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:
3 - 1
x = -----------
2
and
-1
y = ----------
2
The center is at x = 1 and y = -1/2: (1, -1/2).
b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):
diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,
radius = (1/2)√65.
square of the radius = r² = 65/4
The general equation of a circle with center at (h, k) and radius r is
(x - h)² + (y - k)² = r². In this case, the equation is:
(x - 1)² + (y + 1/2)² = 65/4
Step-by-step explanation:
81x⁴ - 16y⁴
(9x²)² - (4y²)²
(9x² + 4y²)(9x² - 4y²)
(9x² + 4y²)(3x + 2y)(3x - 2y)
Answer:Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
x
+
1
4
x
2
-
2
x
-
5
Divide the highest order term in the dividend
4
x
2
by the highest order term in divisor
x
.
4
x
x
+
1
4
x
2
-
2
x
-
5
Multiply the new quotient term by the divisor.
4
x
x
+
1
4
x
2
-
2
x
-
5
+
4
x
2
+
4
x
The expression needs to be subtracted from the dividend, so change all the signs in
4
x
2
+
4
x
4
x
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4
x
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
Pull the next terms from the original dividend down into the current dividend.
4
x
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
Divide the highest order term in the dividend
−
6
x
by the highest order term in divisor
x
.
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
Multiply the new quotient term by the divisor.
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
-
6
x
-
6
The expression needs to be subtracted from the dividend, so change all the signs in
−
6
x
−
6
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
+
6
x
+
6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
+
6
x
+
6
+
1
The final answer is the quotient plus the remainder over the divisor.
4
x
−
6
+
1
x
+
1
Step-by-step explanation:
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